Volumetric haze is showing through solid objects when 'stacked'
Haven't had much luck on this site lately! But I kept banging away at it and figured it out on my own. 



The three overlapping cone shapes that you can see at the 3D window (bottom right), don't come to a point, the point is chopped off. So they're like cylinders that are skinny at the top and fat at the bottom.

The issue was apparently caused by the fact that my cylinders were open-ended (aka non-manifold). They had no faces at the top or bottom. 

So for example in this pic, the first and last cylinders/cones have faces on top. The middle is open. So if I rendered it like this, the middle one would have the problem while the others wouldn't.



So it seems volumetric effects are sensitive to the mesh that contains them. I should have figured that out sooner because I tried making the cones originally with no faces, just 'wireframe' vertices and edges... and the volumetric effect didn't show. They needed faces to contain it. Since the faces have no material, light passes through them ok, so leaving the top of the cones open wasn't necessary.